Geometric Analysis and Mathematical Relativity Seminar——John-Nirenberg Inequality and Collapse in Conformal Geometry
主 题: Geometric Analysis and Mathematical Relativity Seminar——John-Nirenberg Inequality and Collapse in Conformal Geometry
报告人: Professor Yuxiang Li (Tsinghua University)
时 间: 2017-11-27 14:30-16:30
地 点: Room 1418, Science Building No. 1
Let $g$ be a metric over $B$, and $g_k=u_k^\frac{4}{n-2}g$. We assume $\|R(g_k)\|_{L^p}
\frac{n}{2}$. We will use John-Nirenberg inequality to prove that if $vol(B,g_k)\rightarrow 0$, then there exists $c_k\rightarrow +\infty$, such that $c_ku_k$ converges to a positive function weakly in $W^{2,p}_{loc}(B)$. As an application, we will study the bubble tree convergence of a conformal metric sequence with integral-bounded scalar curvature.
